Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
  • G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/008—Surface plasmon devices

Definitions

• Metasurfaces can be described as one- and two-dimensional plasmonic arrays (scat- tering elements) with a periodicity which is small compared to the length of the operating wavelength (subwavelength periodicity). Due to the negligible thickness of these surfaces (ultrathin films) compared to the wavelength of operation, metasurfaces can be considered as an interface of discontinuity enforcing an abrupt change in both the amplitude and phase of the impinging electromagnetic wave.
• an anti-reflective coating can be regarded as a simple metasur- face, as it was first observed by Lord Rayleigh.
• several new metasur- faces have been developed, including plasmonic metasurfaces, metasurfaces based on geometric phases, and metasurfaces based on impedance sheets.
• metasurfaces One of the most important applications of metasurfaces is to control a wavefront of electromagnetic waves by imparting local, gradient phase shifts to the incoming waves, which leads to a generalization of the well known laws of reflection and refraction.
• a metasurface can be used as a planar lens, vortex generator, beam deflector, axicon and so on.
• metasurfaces are also applied in electromagnetic ab- sorbers, polarization converters, and spectrum filters, for wireless communications, energy harvesting, imaging, and cloaking.
• metasurface-based superlenses offer an- other degree of control of the wavefront by using evanescent waves. With surface plasmons in the ultrathin metallic layers, perfect imaging and super-resolution lithog- raphy could be possible, which breaks the common assumption that all optical lens systems are limited by diffraction, a phenomenon called the diffraction limit.
• Classical metasurfaces are artificial sheet materials composed of periodic subwavelength metal/dielectric structures in the horizontal dimensions, which can produce a desired optical wavefront transformation and thereby allows the control of direction, polarization, phase, and amplitude for reflected and transmitted optical fields.
• Metasurface properties require a strong spatial modulation of the light matter interaction strength. This modulation is either achieved using the plasmonic response in metallic antenna structures or with the aid of Mie resonances in dielectric nano- structures (dielectric metamaterials).
• top-down methods which rely on photolithography or electron-beam lithography and following etching, deposition, and lift-off processes
• bottom-up approaches that include laser/ion-beam printing, or self-assembly methods.
• metasurfaces need an additive or subtractive fabrication process and have static functionalities that depend on their fixed geometrical parameters and cannot be changed after fabrication.
• these techniques lead to irreversible modifications of the metasurface material thereby excluding dynamic adaptations/modifications of the metasurface.
• most of these methods are limited to be applied to planar surfaces only, thereby excluding its application to 3D objects.
• an object of the present invention to avoid the above-mentioned disadvantages and to provide for an easier (less process steps) and more flexible method of manufacture of metasurfaces, allowing for a dynamic modification of the metasurface, which inter alia means that the surface modifications are reversible.
• step II a desired to be inside area is defined and delineated on the surface of the substrate which is in the first state of the optical property and wherein subsequently the surface in the defined and delineated inside area is contacted with a liquid which reacts with the substrate material to yield in or to bring about the transition into the at least one second state of the optical property within the inside area only, or wherein in step III the states of the optical property of the surface and the inside area are inverted.
• the process according to the invention has the advantage that no subtractive or additive steps are needed in making the metasurface i.e. the composition of the metasurface is contained entirely within the layer that is transitioned by the liquid. The process, therefore, is cheaper, and the surfaces are smoother than, for example, those formed with photolithography.
• the metasurface is dynamic, i.e the optical property can be reversed or dynamically tuned by the inventive process.
• Another unique advantage of the new process is that it allows metasurfaces to be formed readily on curved or flexible surfaces.
• Metalsurfaces are one- and two-dimensional plasmonic arrays (scattering elements) with a periodicity which is small compared to the length of the operating wavelength (subwavelength periodicity). Due to the negligible thickness of these surfaces (ultrathin films) compared to the wavelength of operation, metasurfaces form an interface of dis- continuity enforcing an abrupt change in both the amplitude and phase of the impinging electromagnetic wave.
• “Substrate” or “phase change material” is a material which undergoes a change in an optical property, such as refraction (refractive index), diffraction, extinction (coefficient), scattering, absorption, reflection, polarization, transmittance, etc.
• the substrate exhibits at least two distinct states of an optical property which are all stable at ambient conditions (i.e. between 10 and 30 °C; between 950 and 1100 hPa).
• the transition from one state of optical property to another is brought about by a change in the chemical composition of the substrate material, e.g. by its stoichiometric oxygen content. This transition may be instigated by applying an electric potential to the liquid.
• VO 2 is an example of a substrate which can be used in the present invention.
• VO 2 is one of the most interesting and widely studied correlated materials, which exhibits a metal-to-insulator phase transition (MIT) as the temperature is reduced below ⁇ 340 K in bulk material.
• MIT metal-to-insulator phase transition
• This phase change is accompanied with a dramatic change in the optica! properties, in metasurfaces consisting of arrays of metal split-ring resonators (SRRs) on a VO 2 layer, the optical performances (e.g. transmissivity and reflectivity) were successfully controlled by temperature variation, THz laser, or voltage induced phase transition. But in all cases the fabrication of the metasurface relied on conventional deposition and lift-off processes.
• SRRs metal split-ring resonators
• ionic liquid gating was shown to suppress the metal-to-insulator transition and stabilize the metallic phase of VO 2 thin films by extraction of a minima! atomic amount of oxygen (about 0.3 atom-%; VO 2 ⁇ VO 1.994 ) under the intense electric field created by polarizing an ionic liquid at the surface of the oxide film.
• ionic liquid gating an ionic liquid is brought into contact with the thin film VO 2 surface and an electric potential is applied between the ionic liquid and an electrode which is also in contact with the ionic liquid.
• the VO 2 surface treated in this way is “gated”, i.e. in the treated areas the metal-to-insulator transition is suppresses and the metallic phase is stabilized.
• the gating effect is highly dependent on the VO 2 crystal facet, which is related to the ease of electric-field-induced motion of oxygen ions along chains of edge- sharing VO 6 octahedra that exist along the rutile c axis.
• the highly face-dependent gating effect only allows the out-of-plane oxygen extraction without notable in-plane diffusion to create sharp structures in the area of contact between the VO 2 substrate surface and ionic liquid.
• the refractive index of the gated VO 2 state is lower than the initial (ungated) one, whereas the extinction coefficient spectrum shifts to longer wavelengths in the gated state. Higher extinction coefficient is observed near the infrared wavelengths for the gated state. All of these changes in optical properties after gating are quite similar to the case when VO 2 is switched from insulating to metallic states by temperature change.
• optical property means an optical property, such as refraction (refractive index), diffraction, extinction (coefficient), scattering, absorption, reflection, polarization, transmittance, etc., all of which can easily be determined and quantified using typical commercial measuring instruments.
• State of optical property means a quantified state of an optical property. Two otherwise identical substrate materials are in a different state of an optical property when they are measurably distinct from each other in this optical property. Measurably distinct means that the optical property varies by a statistically significant amount or factor which is typical for the state transition in question.
• Transition means that the material in question can be converted from one first state of optical property into at least one other second state of optical property, which is measurably distinct from the first state.
• the means for such a transition may be a change in pressure and/or temperature, the application of an electrical field, a chemical reaction etc. Preferably it is a change in the chemical composition of the material, more preferred a change in the oxygen content.
• “Stable” means that state of optical property remains unchanged under ambient conditions for a minimum amount of time.
• Ambient conditions means between 10 and 30 °C and between 950 and 1100 hPa.
• a minimum amount of time means at least 100 days, preferably at least 1000 days, more preferably at least 10000 days.
• “Reversibly” means that the transition from one first state of optical property into another second state of optical property can be reversed from the second state back into the first state.
• An “area” created on a surface of the substrate is a part of the surface which is delineated from another part of the surface by a boundary of infinitesimal width.
• the area may form a closed area having a perimeter of infinitesimal width which delineates the inside of the area from the outside of the area.
• Infinitesimal width means 1-1000 nm, preferably 5-500 nm, more preferred 5-100 nm.
• the liquid can be used as an electrical conducting fluid allowing and/or aiding in the transport of electrons and/or ions to or from the substrate in the area of contact and/or to apply an electrical potential.
• Liquid means a fluid medium, e.g. water, an alcohol like ethanol, methanol etc., a hydrocarbon like pentane, hexane etc., a halogen containing hydrocarbon like chloroform etc., which reacts with the substrate material to yield in or to bring about the transition into the at least one second state of optical property within the exposed inside area(s) only.
• the liquid can be an electrical conducting fluid allowing and/or aiding in the transport of electrons and/or ions to or from the substrate in the exposed area(s) of contact and/or to apply an electrical potential.
• One preferred liquid is an ionic liquid, which is an organic or inorganic liquid which contains or consists of ions.
• Examples are aqueous solutions of organic or inorganic water soluble salts, e.g. NaCI, KCI, etc. or organic ionic liquids like 1-Ethyl- 3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI), 1-Propyl-3- methyl-imidazolium bis(trifluoromethylsulfonyl)imide, 1-Butyl-3-methylimidazolium bis(tri-fluoromethylsulfonyl)imide or 1-Hexyl-3-methylimidazolium bis(trifluoromethyl- sulfonyl)imide.
• These imidazolinium compounds are room temperature ionic liquids (RTIL). They are non-aqueous solvents, which are advantageous over traditional aprotic polar organic solvents in electrochemical reactions. They have a low vapor pressure, high thermal stability and good electrical conductivity.
• the process according to the invention transitions a surface of a substrate into a metasurface.
• the process is able to create plasmonic arrays (scattering elements) on the surface of a phase change material (substrate).
• Liquid gating preferably ionic liquid gating (ILG)
• IDG ionic liquid gating
• the liquid, preferably the ionic liquid brings about a phase change, i.e. a change in an optical property in the local regions under the holes (see Fig. 1a-c).
• This approach is highly flexible, as it does not require physical (subtractive) patterning of the substrate material.
• This approach opens a way towards electrically reconfigurable metamaterials which can act as for instance phased array reflectors.
• the substrate itself is a two dimensional material of negligible thickness (a thin film).
• the thickness is typically in the range of 1-1000 nm, preferably 5-500 nm, more preferably 5-100 nm.
• the planar size of the substrate is typically in the range of 1-1000 mm 2 , preferably 10-500 mm 2 , more preferably 50-299 mm 2 .
• the cross-sectional area of the modified material is defined by the “hole” in the resist layer (the “mask”). Accordingly, it may be desirable for the transition from one state of optical property into another of the substrate to create the substrate surface in a preferred, predetermined direction of a crystallographic face expressed in terms of h,k, l-indices, e.g. the [100] direction, or the [001] direction, or the [111] direction etc.. This may be advantageous if e.g. the mobility of certain atoms in a certain direction of the unit cell ([h,k,l]) of the substrate material is higher/lower than in another direction.
• Such a growth of the thin film in a predetermined direction can be facilitated by epitaxy, where the substrate of interest is grown on an “inducing” surface of a second material which exhibits a physical surface which matches the desired direction [h,k,l] of the to be grown substrate and which exhibits a crystallographic structure and unit cell dimensions which are at least similar, if not close to identical (so called “lattice matching”; i.e. unit cell axis and/or angle deviation of max, 10%, preferably max. 5%, more preferred max. 3%) to the one of the to be grown substrate material.
• Such epitaxy methods are known to the skilled person. It is also possible to form films that are predominantly of one crystal texture but which are not crystallographicaliy oriented with respect to the substrate.
• Polycrystailine films with one preferred crystal orientation perpendicular to the plane of the film can be formed by use of underlayers that themselves grow with a preferred crystalline orientation and that thereby induce the epitaxial growth of the thin film of interest.
• the defined and delineated inside areas are formed on the substrate surface.
• the shapes of the delineated areas can take any desired form which is suitable for the kind of metasurface to be manufactured. E.g. they can be arranged as plasmonic arrays in a series of classic plasmonic V-antennas pattern.
• the shapes are designed and arranged on the surface of the substrate material.
• the predesigned delineated area shapes on the surface in which the state of optical property shall be transitioned from its initial state to a measurably distinct at least second state can be created e.g. by applying lithographic techniques, i.e. by creating a structured mask which covers the to be modified surface of the substrate.
• Typical lithographic resists suitable for exposure using light, electron beams or heat, can be used to cover the surface of the substrate in a thin layer (thickness: 100-1000 nm, preferably 150-750 nm, more preferred 200-400 nm). Subsequently the desired forms of the to be transitioned areas are cut out of the resist cover layer, thereby exposing the substrate surface in the cut out areas only. Cutting can be performed e.g. with precision electron beam lithography methods by use of modification of the chemical properties of the resist layer and their subsequent removal by dissolution by use of suitable chemical solvents.
• the resulting structures can have widths or radii which depend on the wave- length of light the desired metasurface is designed to be operated at of ⁇ 50 nm, preferably ⁇ 25 nm, more preferred ⁇ 10 nm.
• the state of optical property of the exposed area(s) of the substrate surface is (are) transitioned from its initial state of optica! property to a measurably distinct at least second state of optical property.
• the surface in the defined and delineated exposed inside area(s) is (are) contacted with a liquid which reacts with the substrate material to yield in or to bring about the transition into the at least one second state within the exposed inside area(s) only.
• This process is called “liquid gating” since the liquid forms ion “gates” in the exposed surface area(s).
• the liquid can be used as an electrical conducting fluid allowing and/or aiding in the transport of electrons and/or ions to or from the substrate in the exposed area(s) of contact and/or to apply an electrical potential.
• One preferred liquid is an ionic liquid, which is an organic or inorganic liquid which contains or consists of ions.
• Examples are aqueous solutions of organic or inorganic water soluble salts, e.g. NaCI, KCI, etc. or organic ionic liquids like 1-Ethyl- 3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI), 1 -Propyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide, 1-Butyl-3-methylimidazolium bis(tri-fluoromethylsul- fonyl)imide or 1-Hexyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl)imide.
• These imidazolinium compounds are room temperature ionic liquids (RTIL). They are non- aqueous solvents, which are advantageous over traditional aprotic polar organic solvents in electrochemical reactions. They have a low vapor pressure, high thermal stability and good electrical conductivity.
• the transition of state of optical properties is preferably performed by simultaneously applying an electric voltage of 0.1-10 Volts, preferably 1-5 Volts, more preferred 2-4 Volts.
• an electric voltage the voltage is applied against a counter electrode which is also in contact with the ionic liquid.
• a preferred material for the counter electrode is a metal, more preferred a metal like Fe, Co, Ni, Pd, Pt, Cu, Ag, Au or Zn, and most preferred Cu, Ag or Au.
• the reaction time of the liquid with the exposed area(s) is preferably from 1 second to 10 hours, preferably from 1 minute to 1 hour, more preferred from 10 minutes to 40 minutes.
• the structured resist cover layer may be, and preferably is, removed by known techniques, e.g. washing with a solvent and the obtained metasurface can be dried.
• Figure 1 a Electron beam lithography patterning of boomerang-shaped antennas array on VO 2 /TiO 2 .
• Ionic liquid gating on VO 2 /TiO 2 with resist mask on the top.
• Figure 2 a Representative conductive atomic force microscope image, b Amplitude and c phase of near-field optical microscopy images, d Amplitude and e phase of simulated near-field maps for one period of the gated VO 2 boomerang- shaped antennas.
• the periodic length of the array is 16 ⁇ m.
• f The extracted near-field phase at the right-most tip of the boomerang-shaped antennas (blue circles from experimental results c while black square from simulations results e) across one period.
• the black dashed line is the theoretical phase change at different positions.
• Figure 3 a Schematic experimental setup for reflection measurements.
• the incidence angle ( ⁇ ⁇ ) and reflection angle ( ⁇ r ) are marked by black and red arrows.
• the intensity mapping ( ⁇ r versus ⁇ ⁇ ) of far-field reflection for VO 2 thin films b without and c with ionic liquid gating through resist mask at a ⁇ 0 8.05 ⁇ m.
• d Typical simulated phase distribution of x-polarized electric field ( ⁇ Ex ) under the illumination of a normally incident y-polarized EM wave. The corresponding positions of simulated results are marked by red circles in c.
• the dot lines indicate the theoretical prediction of the peak position using the generalized Snell’s law of different orders.
• the anomalous reflections (N - 1) for VO 2 metasurface with different periodic lengths. The incidence angle is fixed at 45°.
• the dashed lines indicate the position of theoretical anomalous reflection positions.
• Figure 8 a Amplitude and b phase of near-field optical microscopy images, c Amplitude and d phase of simulated near-field maps for one period of the gated VO 2 boomerang- shaped antennas.
• the periodic length of the array is 16 ⁇ m.
• the angle between the polarization of incident light and x (or y) axis is 45°.
• Figure 9 a Sketch for the far-field simulation. b-n Simulated Ex field patterns on the x-z plane for a model consisting of metallic V- shape VO 2 array in insulating VO 2 matrix under the illumination of a y-polarized EM wave at different incidence angles from 90° to -30°.
• the scale bar is 8 ⁇ m.
• Such a boomerang-shaped antenna array is chosen to achieve the phase coverage of 2 ⁇ while maintaining large scattering amplitudes.
• a drop of ionic liquid [EMIM-TFSI, (1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide] is applied to the surface of the sample with a resist mask and an isolated gold electrode. Then a gate voltage of +3 V is applied for 0.5 hour between the gold electrode and the
• the change of transport properties caused by ILG is measured in a Hal! bar device with a lateral gate electrode and shown in Fig, 1d.
• a progressive suppression of the MIT in gated VO 2 is observed and the metallic state is kept in the temperature range of 200-340 K.
• the conductivities of the initial (warming branch) and gated VO 2 are 1.83x1o -4 ⁇ cm and 9.92x10 -1 ⁇ cm at 300 K, respectively.
• the metallization is a consequence of the electric-fieid-induced extraction of oxygen ions during the gating.
• optical constants of the VO 2 layer were determined before and after the gating process using an ellipsometer. For this measurement, a 10x10 mm 2 thin film sample was used and after the measurement of the initial state, the sample was gated without any resist mask.
• Figure 1e and f show refractive indices and extinction coefficients of
• the refractive indices of initial and gated VO 2 are very close to each other between 200 and 450 nm.
• the refractive index of gated VO 2 first decreases from 2.92 to 1.51 and then dramatically increases to 7.53 at 10 ⁇ m.
• the refractive index of initial (ungated) VO 2 only shows a gradual decline from 2.64 to 1.98 as the wavelength is changed from 2 to 10 ⁇ m.
• the extinction coefficient of gated VO 2 monotonously rises between 600 nm and 10 ⁇ m to a value of 10.22, while the ungated VO 2 shows an extinction coefficient close to zero for the whole spectral range.
• VO 2 thin film of initial state at 330 K which is higher than the MIT transition temperature
• a very similar refractive index and extinction coefficient spectra was found compared with those of the gated one, confirming the changes of optical constants in the gated sample are related to ILG induced insulator- to-metal transition.
• the ILG was done on the sample through the resist mask to make an array of boomerang-shaped antennas inside the VO 2 layer.
• the sample was affixed to a metal holder by conductive silver paint on the bottom.
• a 1 MW resistor was connected in series with the V02/Nb-doped TiO 2 heterostructure and the CAFM was used to measure the current flowing across the sample (perpendicular to the surface) at a constant voltage of 1 V.
• the leakage current mapping shows one period of boomerang-shaped metallic VO 2 regions in the insulating VO 2 matrix with a periodic length of 16 ⁇ m.
• the highly face-dependent gating effect only allows the out-of-plane oxygen extraction without notable in-plane diffusion to create sharp metallic VO 2 regions in the boomerang- shape.
• These boomerang-shaped conductive regions act as antennas just like those in conventional metasurfaces that are formed from, for example, Au regions on or within a Si host. What is necessary is that the antennas are formed from materials with distinct dielectric coefficients for the relevant wavelength.
• the temperature dependent CAFM results show that the conductive antennas become inactive at 330 K but recovered by cooling the sample down (see Fig. 6).
• the corresponding topography images (not shown) indicate that the conductive regions after gating are slightly higher than the matrix due to the lattice expansion after introducing oxygen vacancies via ILG.
• the metasurface in x-y plane is defined and the unit cell of boomerang- shaped antennas repeat with the periodicity of G in the x direction, while the direction vertical to the metasurface is set to be z. These definitions are applicable to the following geometries of all the measurements. s-SNOM measurement on a sample grown on pure TiO2 (001) substrate
• phase-resolved scattering-type scanning near-field optical microscopy (s-SNOM) is used.
• the experimental results are compared with simulations.
• a period of boomerang-shaped metallic VO 2 regions in the insulating VO 2 matrix with the same shape and size as those in CAFM measurement but grown on pure TiO 2 substrate is used for the s-SNOM measurements.
• a y-polarized incident light beam [wavelength ( ⁇ 0 ) of 6.2 ⁇ m] vertically illuminates the sample from the back side of a double side polished substrate (transmission mode) to get a fully in-plane polarization and resultant lossless phase gradient.
• the results for the structures under purely symmetric and antisymmetric excitation modes are shown in Fig. 8.
• the individual near-field phase ( ⁇ z-exp. and ⁇ z-sim .) images in Fig. 2c and e show gradients along the antenna arms, which are the characteristics of simultaneous excitation of both symmetric and antisymmetric antenna modes.
• the extracted near- field phases at the right-most tip of the boomerang-antennas from both experimental and simulated results exhibit a phase change from about — ⁇ to about ⁇ across the unit cell where the eight antenna data points are summarized in Fig. 2f.
• Such a realization of the phase shifts covering 2 ⁇ range in one unit cell length provides a full control of the wavefront. Similar intensity and phase change can be also observed in the samples with a periodic length of 8 ⁇ m (not shown but similar to Fig. 2).
• a - ⁇ to ⁇ phase change in one period of boomerang-shaped metallic VO 2 antennas is expected to achieve anomalous reflections atfar-field based on the generalized Snell’s law:
• ⁇ r is the reflection angle
• ⁇ i is the incident angle
• ⁇ 0 is the vacuum wavelength
• n i is the refractive index
• the incident light is y-polarized while a polarizer is used to select the anomalous reflection beam that is supposed to be cross-polarized with respect to the excitation.
• the y-polarized incident light is chosen to get a 45° angle with respect to the symmetric axis of each antenna so that both symmetric and antisymmetric modes can be excited and the scattered light has a substantial component polarized orthogonal to that of the incident light with a large range of phases and amplitudes for a given wavelength.
• The is 2 ⁇ /16 ⁇ m-
• n i is set to be 1 for air.
• the simulated reflection light is filtered by a polarizer orthogonal to the polarization of incident light to remove the ordinary reflection.
• Figure 4e summarizes the results of the ordinary and the anomalous reflections for samples with different ⁇ with a fixed incident angle of 45°.
• the sample with smaller ⁇ corresponds to the larger phase gradient and the resultant larger divergence between ordinary and anomalous reflections.
• the positions of anomalous reflections calculated by Eq. 1 are marked by black dotted lines in Fig. 4e, which agree with the experimental data.
• ILG can induce an insulator-to-metal transition followed by dramatic changes in optical properties of VO 2 thin film.
• a metallic phase can be locally created in the insulating parent phase by ILG.
• the metallic VO 2 antenna array with the insulating VO 2 host material realizes a full 2 ⁇ phase manipulation of the optical phase in the near-field and leads to anomalous reflections at far-field consistent with the generalized Snell’s law.
• Such a spatially selective gating engineering represents a new paradigm for active photonic structures and devices.
• the VO 2 films of 20 nm thickness were deposited on (001) oriented pure or 0.5 wt% Nb-doped TiO2 substrate by pulsed laser deposition (PLD) in an oxygen pressure of 1.9x10-2 mbar at 380 °C.
• PLD pulsed laser deposition
• a boomerang-shaped antenna array was designed to excite both symmetric and the antisymmetric modes by y-polarized incident light for all the antennas.
• the boomerang- shaped antennas consist of two rectangular arms with width a, which are connected at the center of one end at an angle D.
• the second four antennas are copies of the first four with rotating clockwise by 90° (Fig. 5).
• the metasurface unit cell containing eight boomerang-shaped antennas will be able to introduce constant phase gradient 2 ⁇ / ⁇ along the x-axis to the light scattered in cross- polarization, where ⁇ is the length of the unit cell in x-axis direction (periodic length). W is the width of the unit ceil in y-axis direction.
• the a of arms in boomerang-shaped antennas is changed from 50 to 500 nm, with corresponding G and W change from 4 to 40 ⁇ m and 0.5 to 5 ⁇ m, respectively.
• Such boomerang-shaped antennas hole arrays are made on the positive resist (ARP 6200.09, Allresist) using electron beam lithography (EBL) (Raith Nanofabrication system). After spin coating at 400 r ⁇ m, ⁇ 200 nm resist was achieved on the surface of sample and then baked at 150 °C for 1 minute. After exposure at a dose of 150 ⁇ C/cm 2 , the sample was developed in AR 600-60 for 30 s. Before ionic liquid gating, the resin was etched using reactive ion etching (PlasmalablOO, Oxford) to slightly remove ⁇ 20 nm residual resist after develo ⁇ ment. Such a pattern could be made in a larger area of 4.8x3.2 mm 2 for the far-field reflection measurements.
• One unit cell of boomerang- shaped antennas with resist pattern is schematically shown in Fig. 5.
• the ionic liquid EMIM-TFSl [1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)- imide], was used for all gating experiments.
• Transistor devices for transport measurements were prepared by photo-lithography and wet etching in the form of Hall-bars with lateral gate electrodes located in the vicinity of the channel. The channel is 400 ⁇ m long and 100 ⁇ m wide. Electrical contacts to the edge of the channel were formed from Au (60 nm)/Cr (10 nm) that was deposited by thermal evaporation.
• the transport properties were carried out in a Quantum Design DynaCool.
• the CAFM function in a Cypher atomic force microscopy (Asylum Research) was used to measure the current flowing across the sample (perpendicular to the surface).
• a 1 M ⁇ resistor was connected in series with the VO 2 /Nb-doped TiO2 at a constant voltage of 2 V.
• a silicon tip with a Ti/lr coating (Asyelec-01) was used (tip radius ⁇ 28 ⁇ 10 nm).
• the optical constants before and after gating were measured by ellipsometry (M-2000 and IR- VASE Ellipsometer from J. A. Wollam).
• a sinusoidal distance modulation results in the generation of high harmonic signal components in the scattered light intensity.
• the scattered light is collected and focused on an MCT-detector.
• a lock-in demodulation at higher harmonics of the tapping frequency ensures an almost background-free measurement.
• Amplitude and phase information in the detected signal are separated with the aid of an interferometric technique. This so called pseudoheterodyne detection involves a Michelson interferometer where the light from the s-SNOM tip interferes with a reference.
• the left four metallic VO 2 antennas are excited in an antisymmetric mode while the right four ones are excited in a symmetric mode, in the amplitude map (Fig. 8a), both the tips and the vertex of each antenna are bright in symmetric mode, while in the antisymmetric mode the vertex stays dark indicating no field buildup at the center.
• a quantum cascade laser with a wavelength 8.05 ⁇ m is used.
• a polarizer allows to select the polarization.
• the sample is mounted on a motorized 360° rotation stage and located at the focus of the telescope. This enables the setting of any incident angle of the laser with respect to the sample surface normal.
• the slight focusing of the incident beam ensures a small spot size on the sample surface.
• the reflected light intensity is measured using a detector mounted on a second 360° rotation stage.
• An aperture in front of the detector is used to increase the angular resolution to the sub-degree range.
• an analyzer (2nd polarizer) in front of the detector can be used to selectively only detect the parallel or the cross-polarized component of the scattered light.
• a mercury cadmium telluride (MCT) detector is used for the mid-infrared light.
• Lock-in amplification is used to increase the dynamic range of the detection.
• an optical chopper located at the inner focal point of the Kepler telescope is used. In this way a dynamic range of about six orders of magnitude is obtained.
• the near-field and far-field simulations for one unit cell of antenna array were performed using the RF module from COMSOL Multiphysics® on a server workstation.

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